The volume of a rectangular box is (x3 - 7x2 - 9x + 63) cubic units. Determine the dimensions of the rectangular box by factoring the volume expression completely.

Hello,

well done.

As x^3-7x²-9x+63 = (x-3) (x+3) (x-7) we must have x>3 and x>-3 and x>7 thus x>7

Explanations:

x^3-7x²-9x+63=x^3-9x + (-7x²+63) = x (x²-9) - 7 (x²-9) = (x²-9) (x-7) = (x+3) (x-3) (x-7)